lognormalfwdrateeulerconstrained.cpp

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
Copyright (C) 2006 Ferdinando Ametrano
Copyright (C) 2006 Mark Joshi
 
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
 
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license.  You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
 
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE.  See the license for more details.
*/
 
#include <ql/models/marketmodels/evolvers/lognormalfwdrateeulerconstrained.hpp>
#include <ql/models/marketmodels/marketmodel.hpp>
#include <ql/models/marketmodels/evolutiondescription.hpp>
#include <ql/models/marketmodels/browniangenerator.hpp>
#include <ql/models/marketmodels/driftcomputation/lmmdriftcalculator.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
 
namespace QuantLib {
 
 
    LogNormalFwdRateEulerConstrained::LogNormalFwdRateEulerConstrained(
                        const ext::shared_ptr<MarketModel>& marketModel,
                        const BrownianGeneratorFactory& factory,
                        const std::vector<Size>& numeraires,
                        Size initialStep)
    : marketModel_(marketModel),
      numeraires_(numeraires),
      initialStep_(initialStep),
      numberOfRates_(marketModel->numberOfRates()),
      numberOfFactors_(marketModel_->numberOfFactors()),
      curveState_(marketModel->evolution().rateTimes()),
      forwards_(marketModel->initialRates()),
      displacements_(marketModel->displacements()),
      logForwards_(numberOfRates_), initialLogForwards_(numberOfRates_),
      drifts1_(numberOfRates_), initialDrifts_(numberOfRates_),
      brownians_(numberOfFactors_), correlatedBrownians_(numberOfRates_),
      alive_(marketModel->evolution().firstAliveRate())
    {
        checkCompatibility(marketModel->evolution(), numeraires);
 
        Size steps = marketModel->evolution().numberOfSteps();
 
        generator_ = factory.create(numberOfFactors_, steps-initialStep_);
        currentStep_ = initialStep_;
 
        calculators_.reserve(steps);
        variances_.reserve(steps);
        fixedDrifts_.reserve(steps);
        for (Size j=0; j<steps; ++j) {
            const Matrix& A = marketModel_->pseudoRoot(j);
            calculators_.emplace_back(A, displacements_, marketModel->evolution().rateTaus(),
                                      numeraires[j], alive_[j]);
            std::vector<Real> fixed(numberOfRates_);
            std::vector<Real> variances(numberOfRates_);
            for (Size k=0; k<numberOfRates_; ++k) {
                Real variance =
                    std::inner_product(A.row_begin(k), A.row_end(k),
                    A.row_begin(k), Real(0.0));
                variances[k] = variance;
                fixed[k] = -0.5*variance;
            }
            variances_.push_back(variances);
            fixedDrifts_.push_back(fixed);
        }
 
        setForwards(marketModel_->initialRates());
    }
 
    const std::vector<Size>& LogNormalFwdRateEulerConstrained::numeraires() const {
        return numeraires_;
    }
 
    void LogNormalFwdRateEulerConstrained::setForwards(const std::vector<Real>& forwards)
    {
        QL_REQUIRE(forwards.size()==numberOfRates_,
                   "mismatch between forwards and rateTimes");
        for (Size i=0; i<numberOfRates_; ++i)
            initialLogForwards_[i] = std::log(forwards[i] +
                                              displacements_[i]);
        calculators_[initialStep_].compute(forwards, initialDrifts_);
    }
 
    void LogNormalFwdRateEulerConstrained::setInitialState(const CurveState& cs) {
        setForwards(cs.forwardRates());
    }
 
    void LogNormalFwdRateEulerConstrained::setConstraintType(
        const std::vector<Size>& startIndexOfSwapRate,
        const std::vector<Size>& endIndexOfSwapRate)
    {
        QL_REQUIRE(startIndexOfSwapRate.size() == numeraires_.size(),
            "Size mismatch in constraint specification.");
        QL_REQUIRE(endIndexOfSwapRate.size() == numeraires_.size(), "Size mismatch in constraint specification.");
 
        startIndexOfSwapRate_=startIndexOfSwapRate;
        endIndexOfSwapRate_ = endIndexOfSwapRate;
 
        covariances_.clear();
        covariances_.reserve(startIndexOfSwapRate_.size());
 
        std::vector<Real> covariances(numberOfRates_);
 
        for (Size i=0; i < startIndexOfSwapRate_.size(); ++i) {
            QL_REQUIRE(startIndexOfSwapRate_[i]+1 == endIndexOfSwapRate_[i],
                "constrained euler currently only implemented for forward rates");
 
            const Matrix& A = marketModel_->pseudoRoot(currentStep_);
 
            for (Size j=0; j < numberOfRates_; ++j) {
                Real cov=0.0;
                for (Size k=0; k < numberOfFactors_; ++k)
                    cov += A[startIndexOfSwapRate_[i]][k]*A[j][k];
                covariances[j] = cov;
 
            }
            covariances_.push_back(covariances);
        }
 
    }
 
    void LogNormalFwdRateEulerConstrained::setThisConstraint(
                                const std::vector<Rate>& rateConstraints,
                                const std::valarray<bool>& isConstraintActive)
    {
        QL_REQUIRE(rateConstraints.size() == numeraires_.size(),
                   "wrong number of constraints specified");
 
        QL_REQUIRE(isConstraintActive.size() == numeraires_.size(),
                   "wrong number of isConstraintActive specified");
 
        rateConstraints_=rateConstraints;
        isConstraintActive_.resize(isConstraintActive.size());
        isConstraintActive_ = isConstraintActive;
 
        for (unsigned long i=0; i < rateConstraints_.size(); i++)
            rateConstraints_[i] = std::log(rateConstraints_[i]+displacements_[i]);
    }
 
 
    Real LogNormalFwdRateEulerConstrained::startNewPath() {
        currentStep_ = initialStep_;
        std::copy(initialLogForwards_.begin(), initialLogForwards_.end(),
                  logForwards_.begin());
        return generator_->nextPath();
    }
 
    Real LogNormalFwdRateEulerConstrained::advanceStep()
    {
        // we're going from T1 to T2
 
        // a) compute drifts D1 at T1;
        if (currentStep_ > initialStep_) {
            calculators_[currentStep_].compute(forwards_, drifts1_);
        } else {
            std::copy(initialDrifts_.begin(), initialDrifts_.end(),
                      drifts1_.begin());
        }
 
        // b) evolve forwards up to T2 using D1;
        Real weight = generator_->nextStep(brownians_);
        const Matrix& A = marketModel_->pseudoRoot(currentStep_);
        const std::vector<Real>& fixedDrift = fixedDrifts_[currentStep_];
 
        Size alive = alive_[currentStep_];
        for (Size i=alive; i<numberOfRates_; i++) {
            logForwards_[i] += drifts1_[i] + fixedDrift[i];
            logForwards_[i] +=
                std::inner_product(A.row_begin(i), A.row_end(i),
                brownians_.begin(), Real(0.0));
        }
 
        // check constraint active
        if (isConstraintActive_[currentStep_]) {
            Size index = startIndexOfSwapRate_[currentStep_];
 
            // compute error
            Real requiredShift =  rateConstraints_[currentStep_] - logForwards_[index];
 
            Real multiplier = requiredShift/variances_[currentStep_][index];
 
            // now shift each rate by multiplier * weighting of index rate
            // across the step
            for (Size i=alive; i<numberOfRates_; i++) {
                // we only need a small part of cov matrix
                logForwards_[i] += multiplier*covariances_[currentStep_][i];
            }
 
            // now we need to calculate the LR shift, we have moved Gaussian Z_k by multiplier * a_{index,k}
            // divide original density by density of shifted normal
            Real weightsEffect = 1.0;
 
            CumulativeNormalDistribution phi;
            for (Size k=0; k < numberOfFactors_; k++) {
                Real shift = multiplier * A[index][k];
                Real originalDensity = phi.derivative(brownians_[k]+shift);
                // the density of the draw after changes in original measure
                Real newDensity = phi.derivative(brownians_[k]);
                // the density of the draw after changes in new measure, shifts cancel
                weightsEffect*= originalDensity/newDensity;
            }
 
            weight *= weightsEffect;
        }
 
        for (Size i=alive; i<numberOfRates_; i++)
            forwards_[i] = std::exp(logForwards_[i]) - displacements_[i];
 
        // c) update curve state
        curveState_.setOnForwardRates(forwards_);
 
        ++currentStep_;
 
        return weight;
    }
 
    Size LogNormalFwdRateEulerConstrained::currentStep() const {
        return currentStep_;
    }
 
    const CurveState& LogNormalFwdRateEulerConstrained::currentState() const {
        return curveState_;
    }
 
}